整數(shù)環(huán)上同態(tài)加密算法及其應用研究
發(fā)布時間：2018-07-22 20:26
【摘要】：隨著互聯(lián)網(wǎng)技術的飛速發(fā)展,大數(shù)據(jù)得到廣泛應用,敏感數(shù)據(jù)的泄露也隨之發(fā)生,網(wǎng)絡安全逐漸受到人們重視。同態(tài)加密算法是大數(shù)據(jù)隱私保護的重要技術之一。同態(tài)加密算法可以對密文進行處理,并且將處理后的新密文正確解密,恢復出明文,減少了敏感信息在網(wǎng)絡中的曝光頻率。同態(tài)加密算法在云計算、密文搜索和電子投票等領域都有廣泛應用。本文利用Gentry構造同態(tài)加密方案的思想,在現(xiàn)有的同類型同態(tài)加密方案的基礎上,對公鑰的生成進行了改進,設計出兩種可以縮短公鑰尺寸的同態(tài)加密方案。首先,針對同態(tài)加密算法中公鑰膨脹過快的問題,結合Dijk等人和代洪艷等人的方案,對SomeWhat方案中公鑰的生成方式進行了改進,構造出處理1bit明文的同態(tài)加密方案。公鑰元素組xi,0和xi,1的生成方式不再采用同一種方式,可以減小公鑰的脆弱性,公鑰個數(shù)由τ+1變?yōu)?(?)τ+1。在計算公鑰元素x0時,引入多項式的選取和計算,用f(p)替代p計算出x0,進一步隱藏了私鑰信息。使用MATLAB實現(xiàn)了新SomeWhat方案和新BootStrappable方案,將具體數(shù)值帶入進行推導演算,證明了新方案的正確性和可行性。并與Dijk等人和代洪艷等人的方案對比,證明新方案擁有最短公鑰尺寸O(λ3.5)。接著,為了提高計算效率,在上述新方案的基礎上,將明文空間從{0,1}擴展到{0,1}l,構造出批量處理明文的同態(tài)加密方案。對選取離散子集的方式進行了改進:將一個具有θ個元素的離散子集,變成兩個具有(?)θ個元素的離散子集,減少了計算量。對新BootStrappable方案中的解密電路進行計算,證明解密電路運算次數(shù)在允許函數(shù)定義的范圍內。并證明了新方案的正確性、同態(tài)性和安全性。將本文構造的方案與CheonJH等人和羅炳聰?shù)热说姆桨笇Ρ?證明新全同態(tài)加密方案擁有最短公鑰尺寸O(λ3.5)。最后,研究了批量處理明文的同態(tài)加密方案在電子投票系統(tǒng)中的應用,在朱正陽等人和王永恒等人的方案上進行改進,構造出能夠批量處理選票的電子投票方案,對選票加密和處理選票的過程進行了改進。密文的處理從t次降為1次。除此之外,本章構造的電子投票方案增加了一個解密系統(tǒng),計票系統(tǒng)負責驗證選票,解密系統(tǒng)負責計算密文選票總和以及解密密文選票,提高了系統(tǒng)工作效率。
[Abstract]:With the rapid development of Internet technology, big data has been widely used, sensitive data leakage has occurred, and network security has been paid more and more attention. Homomorphic encryption algorithm is one of the important technologies of big data privacy protection. The homomorphic encryption algorithm can process ciphertext, and decrypt the processed new ciphertext correctly, restore the plaintext, and reduce the exposure frequency of sensitive information in the network. Homomorphic encryption algorithms are widely used in cloud computing, ciphertext search and electronic voting. In this paper, we use the idea of Gentry to construct homomorphic encryption scheme. Based on the existing homomorphic encryption scheme, we improve the generation of public key, and design two homomorphic encryption schemes which can shorten the size of public key. First of all, aiming at the problem of fast expansion of public key in homomorphic encryption algorithm, combining Dijk et al. And Dai Hongyan's scheme, we improve the way of generating public key in some what scheme, and construct a homomorphic encryption scheme to deal with 1bit plaintext. The generation of public key element groups XING0 and XING1 can reduce the vulnerability of public key, and the number of public keys changes from 蟿 1 to 2 (?) 蟿 1. In the calculation of public key element x0, the selection and calculation of polynomials are introduced, and the information of private key is further hidden by using f (p) instead of p to calculate x0. The new Somewhat scheme and the new Boot Strappable scheme are realized by using MATLAB. The concrete values are brought into the derivation and calculus, and the correctness and feasibility of the new scheme are proved. Compared with Dijk et al and Dai Hongyan schemes, it is proved that the new scheme has the shortest public key size O (位 3.5). Then, in order to improve the computational efficiency, based on the new scheme mentioned above, the plaintext space is extended from {0 ~ 1} to {0 ~ (1)} _ l, and a homomorphic encryption scheme for batch processing of plaintext is constructed. The method of selecting discrete subsets is improved: a discrete subset with 胃 elements is changed into two discrete subsets with 胃 elements, which reduces the computational complexity. The decryption circuit in the new Boot Strappable scheme is calculated, and it is proved that the number of decryption circuit is within the scope of the definition of the permitted function. The correctness, homomorphism and security of the new scheme are proved. Comparing the scheme constructed in this paper with that of Cheon JH et al. And Luo Bingcong et al., it is proved that the new fully homomorphic encryption scheme has the shortest public key size O (位 3.5). Finally, the paper studies the application of homomorphic encryption scheme in batch processing of plaintext in electronic voting system, improves the scheme of Zhu Zhengyang and Wang Yong, and constructs an electronic voting scheme which can process votes in batches. The process of encrypting and processing ballot papers has been improved. The processing of ciphertext was reduced from t to 1. In addition, the electronic voting scheme in this chapter adds a decryption system, the counting system is responsible for verifying the ballot papers, the decryption system is responsible for calculating the total number of the ciphertext ballot papers and decrypting the ciphertext ballot papers, which improves the efficiency of the system.
【學位授予單位】：西南交通大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：TP309.7
本文編號：2138474
[Abstract]:With the rapid development of Internet technology, big data has been widely used, sensitive data leakage has occurred, and network security has been paid more and more attention. Homomorphic encryption algorithm is one of the important technologies of big data privacy protection. The homomorphic encryption algorithm can process ciphertext, and decrypt the processed new ciphertext correctly, restore the plaintext, and reduce the exposure frequency of sensitive information in the network. Homomorphic encryption algorithms are widely used in cloud computing, ciphertext search and electronic voting. In this paper, we use the idea of Gentry to construct homomorphic encryption scheme. Based on the existing homomorphic encryption scheme, we improve the generation of public key, and design two homomorphic encryption schemes which can shorten the size of public key. First of all, aiming at the problem of fast expansion of public key in homomorphic encryption algorithm, combining Dijk et al. And Dai Hongyan's scheme, we improve the way of generating public key in some what scheme, and construct a homomorphic encryption scheme to deal with 1bit plaintext. The generation of public key element groups XING0 and XING1 can reduce the vulnerability of public key, and the number of public keys changes from 蟿 1 to 2 (?) 蟿 1. In the calculation of public key element x0, the selection and calculation of polynomials are introduced, and the information of private key is further hidden by using f (p) instead of p to calculate x0. The new Somewhat scheme and the new Boot Strappable scheme are realized by using MATLAB. The concrete values are brought into the derivation and calculus, and the correctness and feasibility of the new scheme are proved. Compared with Dijk et al and Dai Hongyan schemes, it is proved that the new scheme has the shortest public key size O (位 3.5). Then, in order to improve the computational efficiency, based on the new scheme mentioned above, the plaintext space is extended from {0 ~ 1} to {0 ~ (1)} _ l, and a homomorphic encryption scheme for batch processing of plaintext is constructed. The method of selecting discrete subsets is improved: a discrete subset with 胃 elements is changed into two discrete subsets with 胃 elements, which reduces the computational complexity. The decryption circuit in the new Boot Strappable scheme is calculated, and it is proved that the number of decryption circuit is within the scope of the definition of the permitted function. The correctness, homomorphism and security of the new scheme are proved. Comparing the scheme constructed in this paper with that of Cheon JH et al. And Luo Bingcong et al., it is proved that the new fully homomorphic encryption scheme has the shortest public key size O (位 3.5). Finally, the paper studies the application of homomorphic encryption scheme in batch processing of plaintext in electronic voting system, improves the scheme of Zhu Zhengyang and Wang Yong, and constructs an electronic voting scheme which can process votes in batches. The process of encrypting and processing ballot papers has been improved. The processing of ciphertext was reduced from t to 1. In addition, the electronic voting scheme in this chapter adds a decryption system, the counting system is responsible for verifying the ballot papers, the decryption system is responsible for calculating the total number of the ciphertext ballot papers and decrypting the ciphertext ballot papers, which improves the efficiency of the system.
【學位授予單位】：西南交通大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：TP309.7
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